If you haven't seen it, perhaps you should rent the movie "The Mission" with Robert De Niro and Jeremy Irons. This may help your understanding about how mission work is viewed by many, especially those being "ministered" to.

The first, and most important step, in mission work anywhere is demonstrating a genuine concern for the welfare of the people you are going to help. In order for them to accept your words, they must first believe that your intentions are for their benefit. This requires much labor on your part long before you can ever utter any spiritual advice or counsel. In fact, your entire mission may never involve classic evangelism or ministry. Many such missionarys go to far away places and do nothing but rebuild homes, or help with the irrigation, or provide medical aid, or distribute food. They have no message to proclaim, other than to simply help those less fortunate. This is the most you should expect of your mission, and the best thing you can do is to keep you mouth shut about spiritual matters until long after you have been accepted by the people you are there to help. Remember, "The greatest of these is Charity".

Once you have demonstrated by your deeds and actions that you have something meaningful to offer, then, if the opportunity presents itself, you may gently and gradually enter into religious dialogue. Your initial focus of any discussion should be on all the beneficial similarities your two faiths share. By focusing on the positives this way, you will allow them to become more receptive to your views. Since religion is a faith based experience, you should avoid entering into arguments about "facts". Your facts are not going to match their facts most of the time, at least not at first, but by finding commonalities, you can then get their impressions and opinions on different aspects of their faith, compare them to yours, and start exploring the origins of those views together.

Remember that most missionaries never make it to the discussion phase, so don't push to get there. If God is sending you to these people, it is because they need your help on many levels, and for them, spirituality is at the very bottom of the heap. Becoming their friend first will determine whether or not you have any success at fulfilling your mission. The rest is gravy.

I think you'll find this approach applies to all evangelizing you will ever do in life, whether at home, across the country, or in a far away land. It is also the best model of how Jesus really functioned while he was here.